2 Answers
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There are really three, sort of, but they're not exactly as you described:

Display sleep: The screen goes blank after a certain amount of time. You can wake up the screen by touching the trackpad or pressing a key.

Sleep: In this state, the computer goes to sleep: the hard drive stops spinning and the CPU uses much less (almost no) power. This can be invoked by closing the lid of the laptop, selecting Sleep from the Apple menu, or via a timer. You wake up the computer by opening the lid or pressing a key.

Hibernation: If the battery is almost dead, the laptop will hibernate to save power. This is similar to shutting down, except all the contents of RAM are dumped to the hard drive, which makes it much faster to start up (as well as starting the computer up into the previous state). You have to hit the laptop power key to wake the machine from hibernation.

The LED on the front of the computer (which is not visible on laptop models unless it is lit) can be used to distinguish “display sleep” from the deeper sleep modes. If the screen is dark but the LED is lit and steady then only the display is sleeping. If the LED is fading between off and on (with a rate similar to that of a human breathing), then it is sleeping or hibernating. If the screen is dark and the LED is not lit, the machine is off.
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Chris JohnsenFeb 5 '11 at 4:15

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To clarify, since the October 2004 rev. of Powerbook G4, Mac portables have used Safe Sleep, and always backup the contents of RAM to the Hard Drive when going to sleep, in case the battery is drained while asleep.
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ghoppeJun 9 '11 at 16:42